Transmission line matching



Feb. 17,1942; P. s. C RTER I 2,273,455

TRANSMISSION LINE MATCHING Filed March 14, 1959 h INV A ITOR. pH/up s. CARTER ATTORNEY.

v comparatively wide band Patented F eb. 17,1942

TRANSMISSION LINE MATCHING Philip 8. Carter, Port Jeiierson, N; Y., assignor to Radio Corporation of America,

of Delaware a corporation Application March 14, 1939, Serial No. 261,745

8 Claims. (Cl..17844) The present invention relates to a means for matching a transmission line having a predetermined value of surge impedance with an antenna or a load circuit having a widely different value of impedance. More particularly, the present invention relates to means for matching a transmission line to an antenna whereby the frequency band width of the antenna is not curtailed. Both experience and theory show that when an antenna having a broad frequency characteristic is matched tothe transmission line by means of one of the usual type matching circuits, the frequency band. width is considerably narrowed. The extent of the detrimentaleifect of such a circuit isdirectly proportioned to the ratio of the impedance change.

The present invention relates to methods of, and means for matching a transmission line to a load circuit by means of which the above mentioned difliculty is, for most practical purposes, eliminated.

An object of the present invention is to match present invention wherein 2 quarter wave line sections connected in series are interposed between the transmission line and the load.

Figure 1 shows a transmission line having a surge impedance indicated by Z00, connected to a load having an impedance Z1. equal to sixteen times the impedance Zoo. Connected between the transmission line and load is shown a matching section M having a length equal to a quarter of the length of the operating wave and having a surge impedance ZM equal to four times the surge impedance Zoo of the transmission line.

In Figure 2 the same transmission line and same load are shown as in Figure 1. Interposed between the transmission line and the load .are two impedance matching sections M1 and M2 connected in series and each having a length equal .to a quarter of the length of the operating wave 7 at the midband frequency.

According to my invention the surge imi pedance Z01 of the first matching section M1 is the impedance of an antenna having a broad frequency characteristic to the surge impedance of a transmission line without destroying the irequency characteristic of the antenna.

Another object of the present invention is to provide matching means for the impedance of an antenna to the surge impedance of a-transmission line having a value of surgeimpedance widely different from the impedance of the antenna without restricting the frequency band width of the antenna.

Still another object of the present invention is to provide means. for matching the impedance of one radio frequency impedance of another translating means having a'value of impedance widely different from the impedance of the first translating means without restricting the frequency band width over which said means are operative. I;

Briefly, my invention involves the use of an even number of quarter wave line sections in series between the antenna or other load and the transmission line or other translating means, the ratio of impedances of said sections bearing such a relationship to the ratio of the impedances of .the transmission line and antenna that the transmission line is matched to the load over .a

frequencies. more complete underto the following de- Referring, now, for 'a standing of the inventio tailed description which is accompanied by drawing in which Figure 1 illustrates a method of matching a transmission line to a load circuit having a value of impedance diflerent from the impedance of the transmission line and is shown only for the purposes of explanation; Figure 2 illustrates diagrammatically an example of the made equal to the one-quarterpower of the impedance ratio between, the transmission line and the load or, in the specific example shown in Figure 2, twice the surge impedance of the transmission line. The surge impedance Z02 of the second matching section M2 is made equal to the three-quarter power of the impedance ratio between the transmission line and the load or,

translating means to the in the specific example shown in Figure 2, equal to eight times the impedance of the transmissiop line.

While I have shown the use of two matching sections in Figure 2 it is to be clearly understood that a number of matching sections may be any even number in accordance with the invention.

In the following-detailed mathematical theory of. broad band impedance matching according to my invention, n sections will be considered each section being equal to a quarter of the length of the operating wave at the midband frequency. The number n wfll be considered even in accordance with the invention. Usually two sections (n=2) are suflicient.

If R is the impedance ratio to be changed and if Z01, Z0: .,Z0n are the surge impedances of the quarter wave lines and Zoo the surge im-' pedance of the main line, we make:

At the mid band frequency, where the length] of each section is exactly M4, the section Z02 changes the impedance from RZoo to and the section Z01, from t Zoo.

Let =the ratio of increase in frequency to the mid-band frequency and c=velocity of light.

Then

radians.

on a line section where (K) is the magnitude, the phase angle and exp (M) =4 I is defined by the relation impedance of the transmission line.

From fundamental relations the input impedance Z1 of any line section is For matching section Mix with Zo2=R Zoo and load RZoo and the input impedance Zn of section M2 becomes When p1r is not great so that cos p77 w 1 and sin p'ir r and p1r 1 the above becomes t-ea n] This impedance constitutes the load for the section M1 having a surge-impedance Zo1-K1 for this section is given by:

The input impedance Z11 of section M1 looking x+ .7" .7 =Zoo exp (7'0) which indicates a perfect match with the approximations made. In any case the phase angle introduced into the input impedance of one line section is almost perfectly cancelled by an opposite phase shift due to the action of the other section when working off the mid-band frequency. There is, however, a small decrease in the final input resistance.

A specific case will now be dealt with using the values given in the drawing. Assume a load of 16 times the surge impedance of a main line to be matched thereto. If the matching is done in one step a quarter wave line is used as shown in Figure 1 with a surge impedance equal to 4Zoo where Zoois the surge impedance of the main line. If the frequency is 5 percent highthe input impedance becomes Thus it will be seen that there is introduced a reactive component equal to about 30% of the resistive component. This causes a reflection on the main line of about 15 percent, which is three times the allowable limit of 5% in television practice.

Now suppose the transformation is done in two steps in accordance with the invention and as shown in Figure 2. In this case Zo1=(16) Zoo= 2Zoo and Zo2=(16) Zno=8Zoo. Calculation, without the approximations previously made, shows the final input impedance at a frequency 5 percent high to be Zoo x 0.978/0.08. The reactive component is negligible. The slight miss-match in the resistive component produces a reflection of 1.1% on the main line, and its effect is practically negligible.

While I have shown and particularly described several embodiments of my invention, it is to be distinctly understood that my invention is not limited thereto but that modifications within'the scope of my invention may be made.

I claim: i

1. In combination, a wide band antenna system and a transmission line connected thereto, the impedance of said antenna being R times the surge impedance Zoo of said line, an even number n of matching line sections connected in series and interposed between said antenna and transmission line, each of said sections having a length equal to one-quarter of the length of the operating wave at midband frequency and having surge impedances of Zoi,'Zo2, ratio of the surge impedance of the first of said sections to that of said line being i 3 e 00 (5) 1 and that of the nth section to the line being Zon, the.

2. In combination, a radio frequency load and a transmission line connected therein, the impedance of said load being R times the surge impedance Zoo of said line, ,an even number, n of matching line sections connected in series and interposed between said radio frequency load and transmission line, each of said sections having a length equal to one-quarter of the length of the operating wave at midband frequency and having surge impedances of Z01, Z02, Zon, the

ratio of the surge impedance of the first of said sections to that of said line being that of the second section to said line being a L R (a andthat of the nth section to said line being n1 Z F Z 3. In combination, a radio frequency load and a transmission line connected thereto, the impedance of said load being R times the surge impedance of the transmission line, a pair of quencies removed from midband the reactance introduced by each section is counterbalanced by an opposite reactance introduced by another of said sections, the surge impedance of each of said sections having values between the limits determined by the impedances of said load and said transmission line, the surge impedance of each section beingless than one adjacent inn-=- pedance and greater than the other adjacent im pedance.

6. In combination with a wide band antenna and a transmission line, of means for matching said transmission line to said antenna over said wide band comprising a pair of series connected matching sections interposed between said transmission line and antenna, each having a length equal to one-quarter of the length of the operating wave at midband frequency, the surge imof each of said sections having values between matching line sections connected in series and interposed between said load and transmission line, each of said sections having a length equal to one-quarter of the length of the operating wave at midband frequency, the section adjacent said transmission line having an impedance R times the surge impedance of said transmission line and the second section having an impedance R times the surge impedance of said transmission line.

4. In combination with a wide band antenna system and a transmission line connected thereto, the impedance of said antenna being It times the surge impedance of the transmission line, of means for matching said transmission line to said antenna over said wide band comprising a pair of matching line sections connected in series transmission line, an even number of series conv nected matching sections interposed between said transmission line and load, each havinga length equal to one-quarter of the length of the operating wave at midband frequency, the surge impedance of each of said sections being so proportioned with respect to the ratio of said load impedance to the line impedance that at fre-' the values of impedance of said antenna and the impedance of said transmission line, the surge impedance of each section being less than one adjacent impedance and greater than the other adjacent impedance.

7. In combination, a pair of radio frequency translating elements connected together, the impedance of one of said elements being R times 5 the surge impedance Zoo of the other of said elements, an even number n of matching line sections connected in series and interposed between said elements, each of said sections having a length equal to one quarter of the length of the operating wave and having surge impedances of Z01, Z02, Zo, the ratio of the surge impedahce of each of said sections to the next adjacent impedance progressing from one of said elements to the other of said elements in the relationship one-quarter of the length of the operating frequency at midband frequency, the section adjacent said second translating means having an impedance R times the surge impedance of said second translating means and the second section having an impedance R times the surge impedance of said second translating means.

PHILIP S. CARTER. 

